J.J.Koenderink
Volume 3, No. 1, 1993 Synopsis
In "image understanding" the notion of a (local) "feature" is a fundamental concept. However, the exact meaning of this concept remains essentially unexplained In practice the notion is closely tied up with the concept of a local neighbourhood operator, often called "feature detector". A similar semantic problem arises in electrophysiology where 'receptive fields" play the role of neighbourhood operators and are also often named after"features" ("edge, bar, orientation, movement... detectors"). In psychophysics the notions of "channel" and "texton" are again closely related to the feature idea.
In this paper I analyze the concept of "feature" from first principles and show how this concept can be given an unambiguous meaning. I introduce the concept of a complete assembly, i.e., a group of operators that collectively represent nth-order local geometric structure in a mathematically precise sense. A "feature" can unambiguously be defined as a property that pertains to the structured activity of such assemblies of neighbourhood operators referenced to the space of all possible inputs. The commonly used notion of a "feature detector" cannot be upheld though.